find weather decimal expantion of 13\64 is a terminating or non-terminating decimal. if it terminates, find the number of decimal places its decimal expantion has.
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hello my friend !
we know that a decimal expansion of rational no. p/q terminates when q is of the form of 2^n.5^n
here 64 which is q equals to 2^6.5^0
hence it will terminate
now if we find 13/64
it will terminate after 6 places
I) by division we have 13/64 = 0.203125
ii) look that it's 2^6.5^0 and it will terminate after 6 positions
its true for every power of 2 or 5
hence a no. terminates after the highest power of either 2 or 5
that's because 13/2^6= 13×5^6/2^6×5^6
===. 203125/10^6
=== 203125×10^-6
clearly it will terminate after 6 places of decimal.. because 2 have a power of 6 We needed to extend 5 to the power of 6 and multiply by our no. to get 10^6 finally we multiply by 10^-6 hence we have 6 digit after decimal
we know that a decimal expansion of rational no. p/q terminates when q is of the form of 2^n.5^n
here 64 which is q equals to 2^6.5^0
hence it will terminate
now if we find 13/64
it will terminate after 6 places
I) by division we have 13/64 = 0.203125
ii) look that it's 2^6.5^0 and it will terminate after 6 positions
its true for every power of 2 or 5
hence a no. terminates after the highest power of either 2 or 5
that's because 13/2^6= 13×5^6/2^6×5^6
===. 203125/10^6
=== 203125×10^-6
clearly it will terminate after 6 places of decimal.. because 2 have a power of 6 We needed to extend 5 to the power of 6 and multiply by our no. to get 10^6 finally we multiply by 10^-6 hence we have 6 digit after decimal
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